Volume 7 Number 3 (Jul. 2017)

Finding the Sum of Two Numbers from Their Difference

Pirooz Mohazzabi, Thomas A. Fournelle

Abstract—In a one dimensional random walk of N steps, with a probability p of taking a step to the right, and a probability 1-p of taking a step to the left, it is not possible to determine from the ending position of the walk what N and p are. However, if the N-step random walk is repeated many times then a statistical analysis of the ending positions can be used to estimate both N and p. In this article we present the details of this analysis and test the results by Monte Carlo simulations. These simulations show that very accurate estimates of N and p are obtained even when the number of experimental trials is relatively small.